Finite Group Databasebeta

← #21457338

Subgroups — #21457338

Order 7808.

500 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519796C211yesmaximal, characteristic, complemented
2#16840411C211yesmaximal, characteristic, complemented
3#16840406C211yesmaximal, characteristic, complemented
4#16840153C211yesmaximal, characteristic, complemented
5#16840020C211yesmaximal, characteristic, complemented
6#16839988C211yesmaximal, characteristic, complemented
7#16839975C211yesmaximal, characteristic, complemented
8#16839965C211yesmaximal, characteristic, complemented
9#16839924C211yesmaximal, characteristic, complemented
10#16839921C211yesmaximal, characteristic, complemented
11#16839913C211yesmaximal, characteristic, complemented
12#16839904C211yesmaximal, characteristic, complemented
13#16839874C211yesmaximal, characteristic, complemented
14#16839831C211yesmaximal, characteristic, complemented
15C2×AGL(1,ℤ/8)×C61C211yesmaximal, characteristic, complemented
16C2×#11758224C2211yescharacteristic
17C2×#11758224C2211yescharacteristic, complemented
18#14519796—24no—
19C2×Dic244C2211yescharacteristic, complemented
20C2×#11758202C2211yescharacteristic, complemented
21C2×#11758200C2211yescharacteristic
22C2×#11758200C2211yescharacteristic
23C2×#11758200C2211yescharacteristic, complemented
24C2×C8×D61C2211yescharacteristic, complemented
25#14519775C2211yescharacteristic, complemented
26#14519764C2211yescharacteristic
27#14519760—21no—
28#14519758—21no—
29#14519758—21no—
30#14519756C2211yescharacteristic
31#14519756C2211yescharacteristic
32#14519753C2211yescharacteristic, complemented
33#14519749—21no—
34#14519749—21no—
35#14519748C2211yescharacteristic
36#14519746—21no—
37D4×Dic61C2211yescharacteristic
38D4×Dic61C2211yescharacteristic, complemented
39C4×C22⋊D61C2211yescharacteristic
40C2×#11758196—21no—
41C2×C22⋊Dic61—21no—
42#14519709C2211yescharacteristic, complemented
43#14519706C2211yescharacteristic, complemented
44#14519702C2211yescharacteristic, complemented
45#14519702C2211yescharacteristic, complemented
46#14519701C2211yescharacteristic, complemented
47#14519698C2211yescharacteristic
48#14519698C2211yescharacteristic
49#14519698C2211yescharacteristic, complemented
50C22⋊#92418C2211yescharacteristic
51#14519689C2211yescharacteristic, complemented
52#14519687C2211yescharacteristic, complemented
53C2×#41×C61C2211yescharacteristic
54C22×D4×C61C2211yescharacteristic
55AGL(1,ℤ/8)×C61—24no—
56C2×SD16×C61C2211yescharacteristic
57C2×SD16×C61C2211yescharacteristic
58C2×D8×C61C2211yescharacteristic
59C2×D8×C61C2211yescharacteristic
60C2×M16×C61C2211yescharacteristic
61C24×C61—21no—
62#41×C61—22no—
63#41×C61—41no—
64C2×Q8×C61C2311yescharacteristic
65C2×D4×C61—22no—
66C2×D4×C61—21no—
67C2×D4×C61—21no—
68C2×D4×C61—41no—
69C2×D4×C61C2311yescharacteristic
70C2×D4×C61C2311yescharacteristic
71C2×D4×C61C2311yescharacteristic
72C22×C4×C61—21no—
73C22×C4×C61C2311yescharacteristic
74C2×C22⋊D61—21no—
75C2×C22⋊D61—21no—
76C2×C22⋊D61—21no—
77C2×C22⋊D61D411yescharacteristic
78C22×Dic61—21no—
79C22×Dic61—21no—
80C22×Dic61—21no—
81C22×Dic61—21no—
82#11758224—22no—
83#11758224—22no—
84#11758224—41no—
85#11758224—41no—
86C2×C4×D61C2311yescharacteristic
87C2×Dic122C2311yescharacteristic
88C2×Dic122C2311yescharacteristic
89SD16×C61—22no—
90SD16×C61—22no—
91D8×C61—22no—
92D8×C61D414yescomplemented
93M16×C61—22no—
94C2×C8×C61C2311yescharacteristic
95C2×C8×C61C2311yescharacteristic
96C22⋊Dic61—21no—
97C22⋊Dic61—21no—
98C22⋊Dic61—21no—
99C22⋊Dic61—21no—
100C22⋊Dic61—21no—
101C22⋊Dic61—21no—
102C22⋊Dic61—21no—
103C22⋊Dic61D411yescharacteristic
104#11758202—41no—
105#11758200—22no—
106#11758200—22no—
107#11758200—41no—
108#11758198—21no—
109#11758198D411yescharacteristic
110C4⋊Dic61C2311yescharacteristic
111C4⋊Dic61C2311yescharacteristic
112#11758196—21no—
113#11758196—21no—
114#11758196—21no—
115#11758196—21no—
116#11758196—21no—
117#11758196D411yescharacteristic
118C4×Dic61C2311yescharacteristic
119C2×#92418C2311yescharacteristic
120C2×#92418C2311yescharacteristic
121Dic244—22no—
122C8×D61—22no—
123C23×C61—21no—
124C23×C61—21no—
125C23×C61—21no—
126C23×C61—42no—
127C23×C61—42no—
128C23×C61—81no—
129C23×C61C2×D411yescharacteristic
130C22×D61C2×D411yescharacteristic
131Q8×C61—21no—
132Q8×C61—21no—
133D4×C61—21no—
134D4×C61—21no—
135D4×C61—21no—
136D4×C61—21no—
137D4×C61—42no—
138D4×C61—42no—
139D4×C61C2×D412yes—
140D4×C61C2×D412yes—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—42no—
145C2×C4×C61C2×D411yescharacteristic
146C2×C4×C61C2411yescharacteristic
147C22⋊D61—41no—
148C22⋊D61—42no—
149C22⋊D61—42no—
150C22⋊D61—81no—
151C2×Dic61—21no—
152C2×Dic61—21no—
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61—42no—
156C2×Dic61—42no—
157C2×Dic61—42no—
158C2×Dic61—81no—
159C2×Dic61C2×D411yescharacteristic
160C2×Dic61C2×D411yescharacteristic
161C2×Dic61C2×D411yescharacteristic
162C4×D61—21no—
163C4×D61—21no—
164Dic122—21no—
165Dic122—21no—
166Dic122—21no—
167Dic122—21no—
168C8×C61—21no—
169C8×C61C2×D412yes—
170#92418—21no—
171#92418—21no—
172C22×C61—22no—
173C22×C61—22no—
174C22×C61—21no—
175C22×C61—21no—
176C22×C61—21no—
177C22×C61—41no—
178C22×C61—41no—
179C22×C61—41no—
180C22×C61—41no—
181C22×C61—41no—
182C22×C61—41no—
183C22×C61—41no—
184C22×C61—84no—
185C22×C61C22×D411yescharacteristic
186C2×D61—21no—
187C2×D61—21no—
188C2×D61—21no—
189C4×C61—21no—
190C4×C61—41no—
191C4×C61C22×D411yescharacteristic
192C4×C61H(5,𝔽2)11yescharacteristic
193Dic61—21no—
194Dic61—21no—
195Dic61—21no—
196Dic61—41no—
197Dic61—41no—
198Dic61—41no—
199Dic61—41no—
200#3267—611nomaximal, Sylow
201C2×C61—41no—
202C2×C61—42no—
203C2×C61—42no—
204C2×C61—81no—
205C2×C61D4211yescharacteristic
206C2×C61#57511yescharacteristic
207C2×C61#57711yescharacteristic
208D61—41no—
209C2×AGL(1,ℤ/8)D6111yescharacteristic, complemented
210C2×#135—611no—
211#547—611no—
212#546—611no—
213#497—611no—
214#470—611no—
215#465—611no—
216#463—611no—
217#461—611no—
218#452—611no—
219#452—611no—
220#450—611no—
221#449—611no—
222#442—611no—
223#435—611no—
224C61#326711yescharacteristic, complemented, Sylow
225C2×#41—611no—
226C2×#41—611no—
227C2×#41C2×D6111yescharacteristic
228C22×D4C2×D6111yescharacteristic
229AGL(1,ℤ/8)—24no—
230#135—1224no—
231C2×Q16—611no—
232C2×Q16—611no—
233C2×SD16—611no—
234C2×SD16—611no—
235C2×SD16—611no—
236C2×SD16C2×D6111yescharacteristic
237C2×SD16C2×D6111yescharacteristic
238C2×D8C2×D6111yescharacteristic
239C2×D8C2×D6111yescharacteristic
240C2×M16C2×D6111yescharacteristic
241C22×C8—611no—
242C4⋊Q8—611no—
243#124—611no—
244#123—1221no—
245#123—1221no—
246#123—1221no—
247C22⋊Q8—611no—
248C22⋊Q8—611no—
249C22⋊Q8—611no—
250#121—611no—
251#121—1221no—
252#121—1221no—
253#120—1221no—
254C4×D4—611no—
255C4×D4—611no—
256C4×D4—611no—
257C2×C4⋊C4—1221no—
258C2×C22⋊C4—1221no—
259#106—611no—
260C4⋊C8—611no—
261#103—611no—
262#103—611no—
263#103—611no—
264#102—611no—
265#102—611no—
266#102—611no—
267C22⋊C8—611no—
268C22⋊C8—611no—
269#97—611no—
270C24—21no—
271#41—22no—
272#41—41no—
273#41—1222no—
274#41—1222no—
275#41—2441no—
276#41—2441no—
277C2×Q8—611no—
278C2×Q8—611no—
279C2×Q8C22×D6111yescharacteristic
280C2×D4—22no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—41no—
284C2×D4—611no—
285C2×D4—1221no—
286C2×D4—1221no—
287C2×D4—1221no—
288C2×D4C22×D6111yescharacteristic
289C2×D4C22×D6111yescharacteristic
290C2×D4C22×D6111yescharacteristic
291C22×C4—21no—
292C22×C4—611no—
293C22×C4—1221no—
294C22×C4—1221no—
295C22×C4—1221no—
296C22×C4—1221no—
297C22×C4C22×D6111yescharacteristic
298Q16—1222no—
299Q16—2441no—
300SD16—22no—
301SD16—22no—
302SD16—1222no—
303SD16—1222no—
304SD16—2441no—
305D8—22no—
306D8C22⋊D6114yescomplemented
307M16—22no—
308C2×C8—611no—
309C2×C8—611no—
310C2×C8—1222no—
311C2×C8C22×D6111yescharacteristic
312C2×C8C22×D6111yescharacteristic
313C4⋊C4—611no—
314C4⋊C4—611no—
315C4⋊C4—611no—
316C4⋊C4—1221no—
317C4⋊C4—1221no—
318C4⋊C4—1221no—
319C4⋊C4—1221no—
320C4⋊C4—1221no—
321C22⋊C4—611no—
322C22⋊C4—611no—
323C22⋊C4—1221no—
324C22⋊C4—1221no—
325C22⋊C4—1221no—
326C22⋊C4—1221no—
327C22⋊C4—1221no—
328C22⋊C4—1221no—
329C22⋊C4—1221no—
330C22⋊C4—1221no—
331C42—611no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—42no—
336C23—42no—
337C23—81no—
338C23—611no—
339C23D4×D6111yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—1221no—
343Q8—1221no—
344Q8—1221no—
345Q8—1221no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—42no—
351D4—42no—
352D4—4881no—
353D4—2441no—
354D4—2442no—
355D4—2442no—
356D4C2×C22⋊D6112yes—
357D4C2×C22⋊D6112yes—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—42no—
362C2×C4—611no—
363C2×C4—611no—
364C2×C4—611no—
365C2×C4—1221no—
366C2×C4—1221no—
367C2×C4—1221no—
368C2×C4—1221no—
369C2×C4—1221no—
370C2×C4—1221no—
371C2×C4—4881no—
372C2×C4—2442no—
373C2×C4—2442no—
374C2×C4—2442no—
375C2×C4D4×D6111yescharacteristic
376C2×C4C23×D6111yescharacteristic
377C8—21no—
378C8—1221no—
379C8—1221no—
380C8C2×C22⋊D6112yes—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—22no—
385C22—22no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—84no—
394C22—1221no—
395C22—1221no—
396C22—1221no—
397C22C2×D4×D6111yescharacteristic
398C4—21no—
399C4—41no—
400C4—1221no—
401C4—1221no—
402C4—1221no—
403C4—2441no—
404C4—2441no—
405C4—2441no—
406C4—2441no—
407C4C22×C22⋊D6111yescharacteristic
408C4#1451982211yescharacteristic
409C2—41no—
410C2—42no—
411C2—42no—
412C2—81no—
413C2—2441no—
414C2D4×C22⋊D6111yescharacteristic
415C2#1684055811yescharacteristic
416C2#1684057211yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×AGL(1,ℤ/8)×C61C2
socleC22×C61C22×D4
hypercenterC2×AGL(1,ℤ/8)D61
hypocenterC61#3267
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#14519796C2semidirect
2. #16840411C2semidirect
3. #16840406C2semidirect
4. #16840153C2semidirect
5. #16840020C2semidirect
6. #16839988C2semidirect
7. #16839975C2semidirect
8. #16839965C2semidirect
9. #16839924C2semidirect
10. #16839921C2semidirect
11. #16839913C2semidirect
12. #16839904C2semidirect
13. #16839874C2semidirect
14. #16839831C2semidirect
15. C2×AGL(1,ℤ/8)×C61C2semidirect
17. C2×#11758224C22semidirect
19. C2×Dic244C22semidirect
20. C2×#11758202C22semidirect
23. C2×#11758200C22semidirect
24. C2×C8×D61C22semidirect
25. #14519775C22semidirect
32. #14519753C22semidirect
38. D4×Dic61C22semidirect
42. #14519709C22semidirect
43. #14519706C22semidirect
44. #14519702C22semidirect
45. #14519702C22semidirect
46. #14519701C22semidirect
49. #14519698C22semidirect
51. #14519689C22semidirect
52. #14519687C22semidirect
92. D8×C61D4semidirect
209. C2×AGL(1,ℤ/8)D61semidirect
224. C61#3267semidirect
306. D8C22⋊D61semidirect